(1) Field of the Invention
This invention relates to section reconstruction methods for projecting radiographic data acquired in each scan position, or filtered radiographic data, as back projection data back to a reconstruction area, and various tomography apparatus for use in the medical, industrial and other fields for radiographing patients or objects under examination and reconstructing sectional images thereof. More particularly, the invention relates to a technique for speeding up the back projections in a reconstruction operation.
(2) Description of the Related Art
FIG. 1 shows a conventional X-ray tomography apparatus. The apparatus includes an X-ray focus f and an X-ray detector 42, with an array of X-ray detecting elements, opposed to each other across an object or patient. The X-ray focus f and X-ray detector 42 are rotatable synchronously around the object""s body axis to radiograph the object intermittently from varied angles of X-ray emission to the object. Radiographic data acquired in each scan position is put to a reconstruction operation to reconstruct sectional images of the object.
As a reconstruction method, what is known as FBP (Filtered Back Projection) is often used. The FBP is a method in which radiographic data for a plurality (Np) of images of the object acquired from different scan positions is put to a filtering correction process to produce back projection data s which is projected back to a reconstruction area B virtually set to a site of interest of the object. To determine a pixel value of point b (x, y) in the reconstruction area B, for example, back projection data s (t (x, y, p)) of detector coordinates t (x, y, p) corresponding to a projection to point b (x, y) in a pth scan position is determined and added up the number of times Np. Thus, a total back projection to point b (x, y) is expressed by the following equation (1):                               b          ⁡                      (                          x              ,              y                        )                          =                              ∑                          p              =              0                                                      N                ⁢                                  xe2x80x83                                ⁢                p                            -              1                                ⁢                      s            ⁡                          (                              t                ⁡                                  (                                      x                    ,                    y                    ,                    p                                    )                                            )                                                          (        1        )            
Generally, various parameters are needed to compute detector coordinates t. However, since a scan position is determined by p, the detector coordinates corresponding to the projection to point (x, y) is regarded as t (x, y, p). Further, detector coordinates t (x, y, p) usually is not an integer, and therefore array data s cannot be determined directly. Floating-point interpolation computations are carried out using two adjacent points as shown in FIG. 2. In FIG. 2, u is an integer made by discarding fractional value a of t (x, y, p). An interpolation computation using (u, s (u)) and (u+1, s (u+1)) is expressed by the following equation (2):                               b          ⁡                      (                          x              ,              y                        )                          =                              ∑                          p              =              0                                                      N                ⁢                                  xe2x80x83                                ⁢                p                            -              1                                ⁢                      {                                                            (                                      1                    -                    α                                    )                                xc3x97                                  s                  ⁡                                      (                    u                    )                                                              +                              α                xc3x97                                  s                  ⁡                                      (                                          u                      +                      1                                        )                                                                        }                                              (        2        )            
When a computer performs the above equation (2), a computation as expressed by the following equation (3) is carried out the number of projections (Np times):
b(x, y)=b(x, y)+(1xe2x88x92xcex1)xc3x97s(u)+xcex1xc3x97s(u+1)xe2x80x83xe2x80x83(3)
Though the same computations as equation (3) above, the following equation (4) is actually used to reduce the number of computations:
b(x, y)=b(x, y)+xcex1xc3x97(s(u+1)xe2x88x92s(u))+s(u)xe2x80x83xe2x80x83(4)
The above conventional computations has a disadvantage of involving numerous floating point computations, and thus takes a long time in performing reconstruction after a radiographic operation. Particularly, the interpolating computations with floating point in computing back projections are problematic. A floating point interpolation computational complexity will be described in detail.
First, of the computational expression (4) for one back projection to one point in a reconstruction area, computations for interpolation are listed below.
txe2x86x92u making floating decimals of coordinates into integers . . . one step
u+1 adding integer to coordinates . . . one step
s (u), s (u+1) reading back projection data . . . two steps
xcex1=txe2x88x92u floating point computation of coordinates . . . one step
floating point multiplication of data . . . one step
floating point addition of data . . . two steps
The above computations provide interpolation data to be added to reconstruction point b (x, y). The interpolating computational complexity is eight steps in total. Next, one step is executed for reading b (x, y), then one step for floating point addition to the interpolation value, and finally one step for writing b (x, y) to complete the computations of equation (4). Thus, the computational complexity of equation (4) is 8+3=11 steps in total. The number of computational steps is shown in the column xe2x80x9cequation (4) (1BP)xe2x80x9d in FIG. 7.
The above equation (4) is repeated the number of times corresponding to the number of projections (Np times) to determine a reconstruction pixel value of one point b (x, y). Where the reconstruction area B includes nxc3x97n points, the computational complexity corresponding to equation (4) in all reconstruction computations becomes nxc3x97nxc3x97Np times. This computational complexity is shown in the column xe2x80x9cEquation (4) ALL (all BP)xe2x80x9d in FIG. 7. It will be seen that the total computational complexity in the prior art involves 11xc3x97nxc3x97nxc3x97Np steps, thus requiring a long time for the reconstruction computations.
This invention has been made having regard to the state of the art noted above, and its object is to provide a section reconstruction method and apparatus for speeding up a reconstruction operation.
To fulfill the above object, Inventor has made intensive research and attained the following findings. In the conventional reconstruction computation, data is interpolated in time of the back projection computations. It is time-consuming since the reconstruction requires a great number of floating-point interpolation computations proportional to a product of the number of times of projections Np and the number of section reconstruction pixels (e.g. nxc3x97n points). However, it has been found that interpolation computations repeatedly performed from back projection data far less than the reconstruction points include many similar interpolation computations which may be omitted.
In a solution Inventor has found based on this finding, enlarged interpolation data is obtained by enlarging back projection data by m times by interpolating, and thereafter the enlarged interpolation data is directly projected back to a reconstruction area without interpolation computation. In the back projection computation, the back projection data is selected from the enlarged interpolation data by determining by multiplying projection coordinates of reconstruction points by m. Where the enlargement-rate m is infinite, obviously the computations are the same as in the prior art. A finite enlargement-rate m will cause errors. However, by a suitable value m, excellent quality image is reconstructed and such reconstructed images present no problem. This solution reduces the number of interpolation computations to perform a fast reconstruction.
Based on the above finding, this invention provides section reconstruction methods for projecting radiographic data of an object acquired in each scan position back to a reconstruction area, the method comprising the step of generating enlarged interpolation data by interpolating back projection data and then projecting the enlarged interpolation data back to a two-dimensional or three-dimensional reconstruction area virtually set to a region of interest of the object, the back projection data being radiographic data, or data resulting from filtering of the radiographic data, the radiographic data being acquired in each scan position by causing a radiation source and a detector arranged opposite each other across the object to scan the object synchronously, or to scan the object synchronously with rotation of the object, the radiation source irradiating the object with electromagnetic waves capable of penetrating the object, the detector detecting electromagnetic waves transmitted through the object.
According to this invention, the number of interpolation computations is reduced to the amount corresponding to the enlargement computations by interpolating the back projection data, thereby reducing the section reconstruction computation time.
Preferably, the enlarged interpolation data is generated by an enlargement-rate set to an integer or decimal of at least 1.0. Then, the number of interpolation computations is reduced in proportion to the enlargement rate of the interpolation data, to shorten the reconstruction computation time.
Preferably, the enlarged interpolation data is generated by the enlargement-rate set to at least four times. With this arrangement, while securing an excellent quality of reconstructed images, the number of interpolation computations is reduced in proportion to the rate of enlargement by interpolation of the back projection data, to shorten the reconstruction computation time.
Preferably, when the reconstruction area is an enlarged reconstruction area subdivided to have pixel density exceeding a detector pixel density, the enlarged interpolation data is generated by an enlargement-rate variable in proportion to an enlargement-rate of an enlarged reconstruction area. Though the number of back projection points in the enlarged reconstruction area is increased, the number of interpolation computations hardly increases. As a result, in the case of enlarged reconstruction, the number of interpolation computations is drastically reduced to shorten the reconstruction computation time greatly.
Preferably, when a three-dimensional reconstruction is performed for projecting two-dimensional back projection data to the three-dimensional reconstruction area, two-dimensional enlarged interpolation data is generated by interpolating the two-dimensional back projection data, and the two-dimensional enlarged interpolation data is projected back to the three-dimensional reconstruction area. Even for a three-dimensional reconstruction, the number of interpolation computations is reduced in proportion to the rate of enlargement by interpolating the two-dimensional back projection data, to shorten the reconstruction computation time.
Preferably, the back projection data is enlarged by interpolation by an enlargement-rate variable with directions of back projection. This is effective to prevent quality deterioration in reconstructed images caused by the directions of back projection not parallel to the arrangement of pixels (back projection points) in the section reconstruction area.
Preferably, when the reconstruction area is a reduced reconstruction area reduced to have pixel density less than a detector pixel density, average interpolation data generated by interpolation after taking a moving average of the back projection data is projected back to the reduced reconstruction area. Then, an interpolation process following a moving average of the back projection data provides a fast, reduced reconstruction image while avoiding deterioration in the quality of the reduced reconstruction image. This allows results of the reconstruction to be known quickly.